A simple pendulum of mass m executes S.H.M. w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The total energy of a simple harmonic oscillator is $E = \frac{1}{2} k A^2$,where $A$ is the amplitude.At the extreme position,the phase $\phi = 0

Vedclass · Accepted Answer

$\sqrt{\frac{3 m E}{2}}$

Vedclass · Answer

(B) The total energy of a simple harmonic oscillator is $E = \frac{1}{2} k A^2$,where $A$ is the amplitude.At the extreme position,the phase $\phi = 0$ (or $\pi$). Let the displacement be $x = A \cos(\omega t)$.After a phase shift of $	heta = \frac{\pi}{3}$,the displacement becomes $x = A \cos(\frac{\pi}{3}) = \frac{A}{2}$.The potential energy at this position is $U = \frac{1}{2} k x^2 = \frac{1}{2} k (\frac{A}{2})^2 = \frac{1}{4} (\frac{1}{2} k A^2) = \frac{E}{4}$.The kinetic energy $K$ at this position is $K = E - U = E - \frac{E}{4} = \frac{3E}{4}$.Since kinetic energy $K = \frac{p^2}{2m}$,we have $\frac{p^2}{2m} = \frac{3E}{4}$.Solving for momentum $p$,we get $p^2 = \frac{6mE}{4} = \frac{3mE}{2}$.Therefore,$p = \sqrt{\frac{3mE}{2}}$.

$A$ simple pendulum of mass $m$ executes $S.H.M.$ with total energy $E$. If at an instant it is at one of the extreme positions,then its linear momentum after a phase shift of $\frac{\pi}{3} \, rad$ will be

Similar Questions

The displacement of a particle executing $SHM$ is given by $y = 5 \sin \left(4t + \frac{\pi}{3}\right)$. If $T$ is the time period and the mass of the particle is $2 \text{ g}$, the kinetic energy of the particle when $t = \frac{T}{4}$ is given by (in $\text{ J}$)

The displacement between the position of maximum potential energy and the position of maximum kinetic energy for a particle executing $S.H.M.$ is

In a simple harmonic oscillation,what fraction of total mechanical energy is in the form of kinetic energy,when the particle is midway between mean and extreme position?

$A$ linear harmonic oscillator of force constant $2 \times 10^6\,N/m$ and amplitude $0.01\,m$ has a total mechanical energy of $160\,J$. Which of the following statements is correct?

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal,when displacement (amplitude = $a$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module